Write as an Equation f(x)=3/(x+2)- square root of x-3

$f (x) = \frac{3}{x + 2} - \sqrt{x - 3}$

Rewrite the function as an equation.

$y = \frac{3}{x + 2} - \sqrt{x - 3}$

Simplify $\frac{3}{x + 2} - \sqrt{x - 3}$ .

To write $- \sqrt{x - 3}$ as a fraction with a common denominator, multiply by $\frac{x + 2}{x + 2}$ .

$y = \frac{3}{x + 2} - \sqrt{x - 3} \cdot \frac{x + 2}{x + 2}$

Simplify terms.

Combine $- \sqrt{x - 3}$ and $\frac{x + 2}{x + 2}$ .

$y = \frac{3}{x + 2} + \frac{- \sqrt{x - 3} (x + 2)}{x + 2}$

Combine the numerators over the common denominator.

$y = \frac{3 - \sqrt{x - 3} (x + 2)}{x + 2}$

Simplify the numerator.

Apply the distributive property.

$y = \frac{3 - \sqrt{x - 3} x - \sqrt{x - 3} \cdot 2}{x + 2}$

Multiply $2$ by $- 1$ .

$y = \frac{3 - \sqrt{x - 3} x - 2 \sqrt{x - 3}}{x + 2}$